In cellular communication systems, each mobile terminal needs to stay synchronized with a base station at all times. Each mobile terminal performs an initial synchronization process for establishing synchronization with a base station at the time of power-on or hand-over. In this process, the frame timing of the communication system is detected, and synchronization is established based on the detected frame timing.
FIG. 1 is a drawing illustrating frame exchanges between a base station and a mobile terminal in a TDMA (Time Division Multiple Access) communication system. Tx_at_BS represents a signal transmitted from the base station, and Rx_at_MS represents a signal received by the mobile terminal. Further, Tx_at_MS represents a signal transmitted from the mobile terminal, and Rx_at_BS represents a signal received by the base station.
Frames occur at frame intervals Tf (e.g., 5 ms in the example illustrated in FIG. 1). Each frame is divided into a downlink-DL subframe and an uplink-UL subframe. TTG (Transmit-to-receive Transition Gap) is an interval from the transmission of a downlink subframe to the reception of an uplink subframe performed by the base station. Further, RTG (Receive-to-transmit Transition Gap) is an interval from the reception of an uplink subframe to the transmission of a downlink subframe performed by the base station. SSTTG (Subscriber Station TTG) and SSRTG (Subscriber Station RTG) are TTG and RTG, respectively, on the mobile-terminal side.
Each downlink subframe has a preamble at its beginning. The pattern of such preamble differs from base station to base station. As far as a given base station is concerned, all the subframes transmitted from this base station have the same preamble pattern. Mobile terminals are not informed of the preamble pattern. Mobile terminals thus recognize the start position of each frame by detecting the occurrences of the same pattern at a known frame interval Tf (e.g., 5 ms in the example illustrated in FIG. 1). In order to detect the positions at which the same pattern occurs at the known constant frame interval Tf (e.g., 5 ms in the example illustrated in FIG. 1), a mobile station performs synchronization detection based on auto-correlation.
FIG. 2 is a drawing showing an example of the configuration of a synchronization processing unit utilizing auto-correlation. The synchronization processing unit illustrated in FIG. 2 includes an analog-to-digital converter (ADC) 10, a correlation computing unit 11, a peak-point detecting unit 12, and a plurality of delay elements 13. The correlation computing unit 11 includes a delay element 14, a complex conjugate unit 15, a multiplication unit 16, a moving average unit 17, and an absolute value unit 18.
The analog-to-digital converter 10 converts an analog signal received by an antenna into a digital signal. The correlation computing unit 11 computes the correlation of the digital received signal output from the analog-to-digital converter 10. The correlation value ρ of two complex values x and y is obtained by use of formula (1) as follows.ρ(x,y)=|E(x·y*)|  (1)Here, the function E serves to obtain an expected value. In the case of a signal that changes with time, such an expected value can be acquired by computing a temporal average. y* is the complex conjugate of y.
A received signal y is represented by use of formula (2) as follows.y(k)=h(k)x(k)+n(k)  (2)where:k=0, 1, 2, . . . , Nframe Nframe: Number of Samples for One Framey(k) is a digital received signal for one frame output from the analog-to-digital converter 10. x(k) is a transmitted signal, and h(k) is a channel response function that represents the characteristics of the transmission path. Further, n(k) is noise.
The delay element 14 of the correlation computing unit 11 delays the digital received signal y(k) by Nframe sample points (i.e., the number of sample points in one frame), thereby introducing one-frame time delay. The delayed signal output from the delay element 14 is represented by use of expression (3) as follows.y(k−Nframe)=h(k−Nframe)x(k−Nframe)+n(k−Nframe)  (3)where:h(k−Nframe)=h(k)+Δh(k)Δh(k): Change in Channel ResponseA temporal change in the channel response h(x) is denoted as Δh(k).
The complex conjugate unit 15 obtains y(k−Nframe)* that is the complex conjugate of y(k−Nframe). The multiplication unit 16 then computes the product of y(k−Nframe)* and y(k−Nframe). A temporal average of this product is obtained by the moving average unit 17, thereby obtaining an expected value of product of y(k−Nframe)* and y(k−Nframe). The expected value of this product is represented by use of expression (4) as follows.
                                                                        ɛ                ⁡                                  (                  k                  )                                            =                            ⁢                              E                ⁢                                  ⌊                                                            y                      ⁡                                              (                        k                        )                                                              ·                                                                  y                        ⁡                                                  (                                                      k                            -                                                          N                              frame                                                                                )                                                                    *                                                        ⌋                                                                                                        =                            ⁢                              E                [                                                                            h                      ⁡                                              (                        k                        )                                                              ⁢                                                                  h                        ⁡                                                  (                                                      k                            -                                                          N                              frame                                                                                )                                                                    *                                        ⁢                                          x                      ⁡                                              (                        k                        )                                                              ⁢                                                                  x                        ⁡                                                  (                                                      k                            -                                                          N                              frame                                                                                )                                                                    *                                                        +                                                                                                                      ⁢                                                                    h                    ⁡                                          (                      k                      )                                                        ⁢                                      x                    ⁡                                          (                      k                      )                                                        ⁢                                      n                    ⁡                                          (                                              k                        -                                                  N                          frame                                                                    )                                                                      +                                                                            h                      ⁡                                              (                                                  k                          -                                                      N                            frame                                                                          )                                                              *                                    ⁢                                                            x                      ⁡                                              (                                                  k                          -                                                      N                            frame                                                                          )                                                              *                                    ⁢                                      n                    ⁡                                          (                      k                      )                                                                                  ]                                                          (        4        )            
The absolute value unit 18 computes the absolute value of the expected value obtained by the moving average unit 17. The expected value ε(k) (i.e., the absolute value of the expected value to be exact) corresponding to a sample point k output from the correlation computing unit 11 is supplied to the peak-point detecting unit 12, and is also supplied to the delay elements 13 that are serially cascaded. Each delay element 13 delays the expected value that it receives by one sample point to supply the delayed expected value to the next delay element 13 situated at the following stage, and also supplies this delayed expected value to the peak-point detecting unit 12.
The peak-point detecting unit 12 detects the maximum value among the Nframe expected values ε(k) through ε(k−Nframe+1), and outputs the sample point k that corresponds to this maximum value (which is represented as k with a hat (i.e., circumflex)). Computation that obtains k corresponding to the maximum value is represented by use of expression (5) using ArgMax function as follows.
                              k          ^                =                              ArgMax            k                    ⁡                      (                          ɛ              ⁡                              (                k                )                                      )                                              (        5        )            
When the sample point detected by the peak-point detecting unit 12 correctly matches the position of the preamble symbol, equation (6) as follows is satisfied due to the fact that the preamble symbol appears at an interval equal to Nframe samples. It should be noted that the transmitted signal x(k) is normalized such that its amplitude is equal to 1.x({circumflex over (k)})x({circumflex over (k)}−Nframe)*=1  (6)At the position of the preamble, the transmitted signal x(k) at the sample point k and the transmitted signal x(k−Nframe) situated at the Nframe-th preceding sample point from k are the same complex number. Accordingly, the result of the computation of expression (6) is equal to 1.
Substituting equation (6) into expression (4) for the expected value and expanding the expression by use of the change Δh(k) yield expressions (7), (8), and (9) as follows.
                                                                                                   ɛ                  ⁡                                      (                                          k                      ^                                        )                                                  =                                ⁢                                  E                  ⁡                                      [                                                                                                                                                                                      h                                ⁡                                                                  (                                                                      k                                    ^                                                                    )                                                                                            ⁢                                                                                                h                                  ⁡                                                                      (                                                                                                                  k                                        ^                                                                            -                                                                              N                                        frame                                                                                                              )                                                                                                  ⋆                                                                                      +                                                                                          h                                ⁡                                                                  (                                                                      k                                    ^                                                                    )                                                                                            ⁢                                                              x                                ⁡                                                                  (                                                                      k                                    ^                                                                    )                                                                                            ⁢                                                              n                                ⁡                                                                  (                                                                                                            k                                      ^                                                                        -                                                                          N                                      frame                                                                                                        )                                                                                                                      +                                                                                                                                                                                                                                          h                                ⁡                                                                  (                                                                                                            k                                      ^                                                                        -                                                                          N                                      frame                                                                                                        )                                                                                            ⋆                                                        ⁢                                                                                          x                                ⁡                                                                  (                                                                                                            k                                      ^                                                                        -                                                                          N                                      frame                                                                                                        )                                                                                            ⋆                                                        ⁢                                                          n                              ⁡                                                              (                                                                  k                                  ^                                                                )                                                                                                                                                                          ]                                                                                                                          =                                ⁢                                  E                  ⁡                                      [                                                                                                                                                                                                                                                        h                                  ⁢                                                                      (                                                                          k                                      ^                                                                        )                                                                                                                                                              2                                                        +                                                                                          h                                ⁡                                                                  (                                                                      k                                    ^                                                                    )                                                                                            ⁢                              Δ                              ⁢                                                                                                                          ⁢                                                                                                h                                  ⁡                                                                      (                                                                          k                                      ^                                                                        )                                                                                                  ⋆                                                                                      +                                                          h                              ⁢                                                              (                                                                  k                                  ^                                                                )                                                            ⁢                                                              x                                ⁡                                                                  (                                                                      k                                    ^                                                                    )                                                                                            ⁢                                                              n                                ⁡                                                                  (                                                                                                            k                                      ^                                                                        -                                                                          N                                      frame                                                                                                        )                                                                                                                      +                                                                                                                                                                                                                                          h                                ⁡                                                                  (                                                                                                            k                                      ^                                                                        -                                                                          N                                      frame                                                                                                        )                                                                                            ⋆                                                        ⁢                                                                                          x                                ⁡                                                                  (                                                                                                            k                                      ^                                                                        -                                                                          N                                      frame                                                                                                        )                                                                                            ⋆                                                        ⁢                                                          n                              ⁡                                                              (                                                                  k                                  ^                                                                )                                                                                                                                                                          ]                                                                                                                          =                                ⁢                                  E                  ⁡                                      [                                                                                                                                                  h                            ⁡                                                          (                                                              k                                ^                                                            )                                                                                                                                2                                            +                                              δ                        ⁢                                                                                                  ⁢                                                  h                          ⁡                                                      (                                                          k                              ^                                                        )                                                                                              +                                              w                        ⁡                                                  (                                                      k                            ^                                                    )                                                                                      ]                                                                                                          (        7        )                                          δ          ⁢                                          ⁢                      h            ⁡                          (              k              )                                      =                              h            ⁡                          (              k              )                                ⁢          Δ          ⁢                                          ⁢                                    h              ⁡                              (                k                )                                      *                                              (        8        )            w(k)=h(k)x(k)n(k−Nframe)+h(k−Nframe)*x(k−Nframe)*n(k)  (9)
Expression (8) represents an error attributable to channel fluctuation. Expression (9) represents an error attributable to the noise n(k) that is input into the correlation computing unit 11.
As described above, the expected value computed by the correlation computing unit 11 illustrated in FIG. 2 includes the channel-fluctuation-attributable error and the noise-attributable error These errors may increase to such a level that cannot be ignored relative to the gain of the correlation computation. When this happens, the synchronization processing unit illustrated in FIG. 2 cannot correctly detect the position of a preamble.
The gain of correlation computation is proportional to the number of samples taken for the correlation computation. The gain of correlation computation is equal to a ratio of the preamble symbol period to the sampling period. In the case of the WiMAX system having a bandwidth of 5 MHz, for example, a ratio of the preamble symbol period to the sampling period is equal to 576 as demonstrated below. In such a case, gain Gcorr of correlation computation is equal to 27.6 decibel as demonstrated by expression (10) shown below.
                              G          corr                =                ⁢                              B            ⁢                                                  ⁢            W            ×            n            ×                                          N                                  F                  ⁢                                                                          ⁢                  F                  ⁢                                                                          ⁢                  T                                            ⁡                              (                                  1                  +                  G                                )                                                          B            ⁢                                                  ⁢            W            ×            n                                                  =                ⁢                                            5.0              ⁢              E                        +                          6              ×                              (                                  28                  /                  25                                )                            ×              512              ⁢                              (                                  1                  +                                      (                                          1                      /                      8                                        )                                                  )                                                                        5.0              ⁢              E                        +                          6              ×                              (                                  28                  /                  25                                )                                                                            =                ⁢        576                            where:        
                              B          ⁢                                          ⁢          W          ⁢                      :                    ⁢                                          ⁢          Nominal          ⁢                                          ⁢          Channel          ⁢                                          ⁢          Bandwidth                ⁢                                  ⁢                  n          ⁢                      :                    ⁢                                          ⁢          Sampling          ⁢                                          ⁢          Factor                ⁢                                  ⁢                              N                          F              ⁢                                                          ⁢              F              ⁢                                                          ⁢              T                                ⁢                      :                    ⁢                                          ⁢          F          ⁢                                          ⁢          F          ⁢                                          ⁢          T          ⁢                                          ⁢          Size                ⁢                                  ⁢                  G          ⁢                      :                    ⁢                                          ⁢          CP          ⁢                                          ⁢          Ratio                ⁢                                  ⁢                                                                                                  G                    corr                                    ⁢                                                                          [                  dB                  ]                                =                                ⁢                                  10                  ×                  log                  ⁢                                                                          ⁢                  10                  ⁢                                      (                    576                    )                                                                                                                          =                                ⁢                                  27.6                  ⁢                                                                          [                  dB                  ]                                                                                        (        10        )            The errors obtained as expressions (8) and (9) may be sufficiently large relative to the gain of correlation computation as given by expression (10). That is, the mobile terminal may be moving, and the signal-to-noise ratio may be low. In such a case, the synchronization processing unit fails to detect a correct synchronization point.    [Patent Document 1] Japanese Patent Application Publication No. 8-265236    [Patent Document 2] Japanese Patent Application Publication No. 2006-191187